The Evaluation of Moments of Bounded Regions Using Spline Approximations of the Boundary

The subject of this paper is the computation of the first three moments of bounded regions imbedded in 2- and 3-dimensional Euclidean spaces. The method adopted here is based upon formulae derived elsewhere, that permit the computation of the said moments — volume, vector first moment and inertia tensor — via integration along the boundary. This is accomplished by the application of Gauss Divergence Theorem to planar and axially-symmetric 3-D regions. It is shown that a spline approximation of the boundary leads to explicit, readily implementable formulae. Two examples are included to illustrate the applicability of the procedure.